A rectangular sports field has dimensions 150 m × 120 m. Its length is…
2023
A rectangular sports field has dimensions 150 m × 120 m. Its length is increased by 0.8% and its width is reduced by 0.5%. What is the percent change in the area of the field?
Answer: A. ~0.3% — ConceptWhen two dimensions change by a% and b%, the area multiplier is (1 + a/100)(1 + b/100), with a decrease represented by a negative rate. Equivalently,…
- A.
~0.3%
- B.
~0.4%
- C.
~1.3%
- D.
~1.6%
Show answer & explanation
Correct answer: A
Concept
When two dimensions change by a% and b%, the area multiplier is (1 + a/100)(1 + b/100), with a decrease represented by a negative rate. Equivalently, the net percentage change is a + b + ab/100.
The product term matters because both dimension changes act successively on the area.
Application
The original area is 150 × 120 = 18,000 m².
The new length is 150 × 1.008 = 151.2 m.
The new width is 120 × 0.995 = 119.4 m.
The new area is 151.2 × 119.4 = 18,053.28 m².
The increase is 18,053.28 − 18,000 = 53.28 m², so the percentage increase is (53.28/18,000) × 100 = 0.296%.
Cross-check
Using successive percentage change directly, 0.8 + (−0.5) + [0.8 × (−0.5)]/100 = 0.3 − 0.004 = 0.296%. This agrees with the area calculation.
Result
The area increases by 0.296%, which rounds to approximately 0.3%.